Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains. (English) Zbl 1425.35126
J. Spectr. Theory 9, No. 3, 857-895 (2019); erratum ibid. 11, No. 4, 1987-1991 (2021).
The paper deals with shape optimization for spectral problems. Specifically, a two-parameter family of spectral shape optimization problems for the Dirichlet Laplacian is studied. The optimization is restricted to certain classes of convex domains. Results on the existence of extremal domains and asymptotic behavior are obtained.
Reviewer: Dumitru Motreanu (Perpignan)
MSC:
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 47A75 | Eigenvalue problems for linear operators |
| 49Q10 | Optimization of shapes other than minimal surfaces |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
Keywords:
shape optimization; Riesz eigenvalue means; eigenvalue sums; Dirichlet-Laplace operator; Weyl asymptotics; convexityReferences:
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